Find the Derivative - d/dx xsin(x)

Problem

ddx⁢x⁢sin⁡x d over d x x sine x

Solution

  1. Identify the rule needed for the expression, which is a product of two functions: u=x u equals x and v=sin⁡x v equals sine x

  2. Apply the product rule formula, which states d(u)⁢vdx=u⁢dvdx+v⁢dudx d of u v over d of x equals u d of v over d of x plus v d of u over d of x

  3. Differentiate the individual components: dxdx=1 d x over d x equals 1 and dsin⁡xdx=cos⁡x d sine x over d x equals cosine x

  4. Substitute these derivatives back into the product rule formula.

  5. Simplify the resulting expression to find the final derivative.

Final Answer

d(x)⁢sin⁡xdx=x⁢cos⁡x+sin⁡x d of x sine x over d of x equals x cosine x plus sine x

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